Knit Product of Finite Groups and Sampling Articles uri icon

publication date

  • December 2019

start page

  • 1

end page

  • 16

issue

  • 6

volume

  • 16

International Standard Serial Number (ISSN)

  • 1660-5446

Electronic International Standard Serial Number (EISSN)

  • 1660-5454

abstract

  • A finite sampling theory associated with a unitary representation of a finite non-abelian group G on a Hilbert space is established. The non-abelian group G is a knit product N⋈H of two finite subgroups N and H where at least N or H is abelian. Sampling formulas where the samples are indexed by either N or H are obtained. Using suitable expressions for the involved samples, the problem is reduced to obtain dual frames in the Hilbert space ℓ2(G) having a unitary invariance property; this is done by using matrix analysis techniques. An example involving dihedral groups illustrates the obtained sampling results.

keywords

  • dual frames; finite frames; finite unitary-invariant subspaces; knit product of groups; left-inverses; sampling expansions; unitary representation of a group